Gradients of Pearson Correlation for the Analysis of Biomedical Data

In biomedical analytics correlation is one of the major criteria for the characterization of similarities between measured data items. It is demonstrated how the formal derivative of Pearson correlation can be used for gradient-based optimization of data models. Firstly, individual data attributes can be rated according to their impact on pairwise data relationships, analogous to the variance measure in Euclidean space. Secondly, a versatile visualization method is presented which performs multi-dimensional scaling from high-dimensional source data to low-dimensional target space by maximizing correlation between distances of source and adaptive target data. As shown for mass spectroscopy data, a combination of attribute rating and data visualization helps revealing interesting data properties.